$\gamma^\ast \gamma \to \eta, \eta^\prime$ transition form factors

TL;DR

This paper calculates the transition form factors for $ o ext{eta, eta'}$ mesons across all spacelike momenta using a continuum approach, incorporating the non-Abelian anomaly, and compares results with experimental data.

Contribution

It introduces a novel model for the non-Abelian anomaly contribution in the Bethe-Salpeter kernel for $ ext{eta, eta'}$ mesons and provides comprehensive predictions for their transition form factors.

Findings

Results agree well with existing experimental data.

Highlights the importance of QCD evolution at large $Q^2$ especially for $ ext{eta'}$.

Provides insights into the quark distribution amplitudes within $ ext{eta, eta'}$.

Abstract

Using a continuum approach to the hadron bound-state problem, we calculate $\gamma^\ast \gamma \to \eta, \eta^\prime$ transition form factors on the entire domain of spacelike momenta, for comparison with existing experiments and in anticipation of new precision data from next-generation $e^+ e^-$ colliders. One novel feature is a model for the contribution to the Bethe-Salpeter kernel deriving from the non-Abelian anomaly, an element which is crucial for any computation of $\eta, \eta^\prime$ properties. The study also delivers predictions for the amplitudes that describe the light- and strange-quark distributions within the $\eta, \eta^\prime$. Our results compare favourably with available data. Important to this at large-$Q^2$ is a sound understanding of QCD evolution, which has a visible impact on the $\eta^\prime$ in particular. Our analysis also provides some insights into the properties of $\eta, \eta^\prime$ mesons and associated observable manifestations of the non-Abelian anomaly.